Fluids

With the development of mature Computational Fluid Dynamics (CFD) tools for fluids (air and liquid) and Finite Element Methods (FEM) for solids and structures, many approaches have been proposed to tackle the so-called Fluid–Structure Interaction or Fluid–Solid Interaction (FSI) problems. Traditional partitioned iterations are often used to link available FEM codes with CFD codes in the study of FSI systems. Although these procedures are convenient, fluid mesh adjustments according to the motion and finite deformation of immersed solids or structures can be challenging or even prohibitive. Moreover, complex dynamic behaviors of coupled FSI systems are often lost in these iterative processes. In this paper, the author would like to review the so-called monolithic approaches for the solution of coupled FSI systems as a whole in the context of the immersed boundary method. In particular, the focus is on the implicit monolithic algorithm for compressible solids immersed inside a compressible liquid. Notice here the main focus of this paper is on liquid or more precisely liquid phase of water as working fluid. Using the word liquid, the author would like to emphasize the consideration of the compressibility of the fluid and the assumption of constant density and temperature. It is a common practice to assume that the pressure variations are not strong enough to alter the liquid density in any significant fashion for acoustic fluid–solid interactions problems. Although the algorithm presented in this paper is not directly applicable to aerodynamics in which the density change is significant along with its relationship with the pressure and the temperature, the author did revisit his earlier work on merging immersed boundary method concepts with a fully-fledged compressible aerodynamic code based on high-order compact scheme and energy conservative form of governing equations. In the proposed algorithm, on top of a uniform background (ghost) mesh, a fully implicit immersed method is implemented with mixed finite element methods for compressible liquid as well as immersed compressible solids with a matrix-free Newton–Krylov iterative solution scheme. In this monolithic approach, with the simple modulo function, the immersed solid or structure points can be easily located and thus the displacement projections and force distributions stipulated in the immersed boundary method can be effectively and efficiently implemented. This feature coupled with the key concept of the immersed boundary method helps to avoid topologically challenging mesh adjustments and to incorporate parallel processing commands such as Message Passing Interface (MPI) and further vectorization of the numerical operation. Once these high-performance procedures are implemented coupled with the monolithic implicit matrix-free Newton–Krylov iterative scheme with immersed methods, effective and efficient reduced order modeling techniques can then be employed to explore phase and parametric spaces. The in-house developed programs are at the moment two-dimensional. Furthermore, based on the same approach implemented in one-dimensional test example with one continuum immersed in another continuum, such monolithic implicit matrix-free Newton–Krylov iterative approach can be extended for the study of composites with deformable aggregates and matrix. Full article

This work discusses in vivo experiments that were performed to evaluate whether local or whole-body heating to 40 °C reduced interstitial fluid pressures (IFPs) and enhanced nanoparticle delivery to subcutaneous PC3 human prostate cancer xenograft tumors in mice. After heating, 0.2 mL of a previously developed nanofluid containing gold nanoparticles (10 mg Au/mL) was injected via the tail vein. The induced whole-body hyperthermia led to increases in tumor and mouse body blood perfusion rates of more than 50% and 25%, respectively, while the increases were much smaller in the local heating group. In the whole-body hyperthermia groups, the IFP reduction from the baseline at the tumor center immediately after heating was found to be statistically significant when compared to the control group. The 1 h of local heating group showed IFP reductions at the tumor center, while the IFPs increased in the periphery of the tumor. The intratumoral gold nanoparticle accumulation was quantified using inductively coupled plasma mass spectrometry (ICP-MS). Compared to the control group, 1 h or 4 h of experiencing whole-body hyperthermia resulted in an average increase of 51% or 67% in the gold deposition in tumors, respectively. In the 1 h of local heating group, the increase in the gold deposition was 34%. Our results suggest that 1 h of mild whole-body hyperthermia may be a cost-effective and readily implementable strategy for facilitating nanoparticle delivery to PC3 tumors in mice. Full article

This paper presents an analysis of linear viscous stress Favre averaged turbulence models for computational fluid dynamics (CFD) of fully turbulent round jets with a long straight tube geometry in the near field. Although similar work has been performed in the past with very relevant solutions, considerations were not given for the issues and limitations involved with coupling between an Eulerian and Lagrangian phase, such as in fully two-way coupled CFD-DEM. These issues include limitations on solution domain, mesh cell size, wall modelling, and momentum coupling between the two phases in relation to the particles size. Therefore, within these considerations, solutions are provided to the Navier–Stokes equations with various turbulence models using a three-dimensional wedge long straight tube geometry for fully developed turbulence flow. Simulations are performed with a Reynolds number of 13,000 and 51,000 using two different tube diameters. It is found that a modified k-$\epsilon$ turbulence model achieved the most agreeable results for both the velocity and turbulent flow fields between these two flow regimes, while a modified k-$\omega$ SST/BSL also provided suitable results. Full article

This study presents an evaluation of semi-empirical single-point wall pressure spectrum models by comparing model predictions with wind tunnel and flight test data. The mean squared error was used to compare the power spectral density of the wall pressure fluctuations predicted by semi-empirical models with a large amount of experimental data. Results show that the models proposed by Goody and Smol’yakov have the lowest mean squared error when predicting the power spectral density for wind tunnel experiments and the Rackl and Weston model has the lowest mean squared error when predicting the power spectral density for flight test data. In addition, although current studies of the power spectra obtained in the wind tunnel are similar, they are not generally an accurate representation of flight test experiments. Full article

In this paper, known probabilistic methods for estimating the thickness of the boundary layer of a two-dimensional laminar flow of viscous incompressible fluid are extended to three-dimensional laminar flows of a viscous compressible medium. Their applicability to the problems of boundary-layer stability is studied with the $\mathrm{LOTRAN}3$ software package, which allows us to compute the position of laminar-turbulent transition in three-dimensional aerodynamic configurations. Full article

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L² errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state). Full article

Parallel sidewalls are the standard bounding walls in wind tunnels when making a wind tunnel model for free-flight condition. The consequence of confinement in wind tunnel tests, known as wall-interference, is one of the main sources of uncertainty in experimental aerodynamics, limiting the realizability of free-flight conditions. Although this has been an issue when designing transonic wind tunnels and/or in cases with large blockage ratios, even subsonic wind tunnels at low-blockage-ratios might require wall corrections if a good representation of free-flight conditions is intended. In order to avoid the cumbersome streamlining methods especially for subsonic wind tunnels, a sensitivity analysis is conducted in order to investigate the effect of inclined sidewalls as a reduced-order wall insert in the airfoil plane. This problem is investigated via Reynolds-averaged Navier–Stokes (RANS) simulations, and a NACA4412 wing at the angles of attack between 0 and 11 degrees at a moderate Reynolds number (400 k) is considered. The simulations are validated with well-resolved large-eddy simulation (LES) results and experimental wind tunnel data. Firstly, the wall-interference contribution in aerodynamic forces, as well as the local pressure coefficients, are assessed. Furthermore, the isolated effect of confinement is analyzed independent of the boundary-layer growth. Secondly, wall-alignment is modified as a calibration parameter in order to reduce wall-interference based on the aforementioned assessment. In the outlined method, we propose the use of linear inserts to account for the effect of wind tunnel walls, which are experimentally simple to realize. The use of these inserts in subsonic wind tunnels with moderate blockage ratio leads to very good agreement between free-flight and wind tunnel data, while this approach benefits from simple manufacturing and experimental realization. Full article

A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids. Full article

We consider the estimation of parameter-dependent statistics of functional outputs of steady-state convection–diffusion–reaction equations with parametrized random and deterministic inputs in the framework of linear elliptic partial differential equations. For a given value of the deterministic parameter, a stochastic Galerkin finite element (SGFE) method can estimate the statistical moments of interest of a linear output at the cost of solving a single, large, block-structured linear system of equations. We propose a stochastic Galerkin reduced basis (SGRB) method as a means to lower the computational burden when statistical outputs are required for a large number of deterministic parameter queries. Our working assumption is that we have access to the computational resources necessary to set up such a reduced-order model for a spatial-stochastic weak formulation of the parameter-dependent model equations. In this scenario, the complexity of evaluating the SGRB model for a new value of the deterministic parameter only depends on the reduced dimension. To derive an SGRB model, we project the spatial-stochastic weak solution of a parameter-dependent SGFE model onto a reduced basis generated by a proper orthogonal decomposition (POD) of snapshots of SGFE solutions at representative values of the parameter. We propose residual-corrected estimates of the parameter-dependent expectation and variance of linear functional outputs and provide respective computable error bounds. We test the SGRB method numerically for a convection–diffusion–reaction problem, choosing the convective velocity as a deterministic parameter and the parametrized reactivity or diffusivity field as a random input. Compared to a standard reduced basis model embedded in a Monte Carlo sampling procedure, the SGRB model requires a similar number of reduced basis functions to meet a given tolerance requirement. However, only a single run of the SGRB model suffices to estimate a statistical output for a new deterministic parameter value, while the standard reduced basis model must be solved for each Monte Carlo sample. Full article

Gas–liquid two-phase flow is widely used in many engineering fields, and bubble dynamics is of vital importance in optimizing the engineering design and operating parameters of various adsorptive bubble systems. The characteristics of gas–liquid two-phase (e.g., bubble size, shape, velocity, and trajectory) remain of interest because they give insight into the dynamics of the system. Bubble plumes are a transport phenomenon caused by the buoyancy of bubbles and are capable of generating large-scale convection. The surface flow generated by bubble plumes has been proposed to collect surface-floating substances (in particular, oil layers formed during large oil spills) to protect marine systems, rivers, and lakes. Furthermore, the surface flows generated by bubble plumes are important in various types of reactors, engineering processes, and industrial processes involving a free surface. The bubble parameters play an important role in generating the surface flow and eventually improving the flow performance. This paper studies the effects of temperature on bubble parameters and bubble motion to better understand the relationship between the various bubble parameters that control bubble motion and how they impact the formation of surface flow, with the ultimate goal of improving the efficiency of the generation of surface flow (i.e., rapidly generate a strong, high, and wide surface flow over the bubble-generation system), and to control the parameters of the surface flow, such as thickness, width, and velocity. Such flow depends on the gas flow rate, bubble size (mean bubble diameter), void fraction, bubble velocity, the distance between bubble generator and free surface (i.e., water height), and water temperature. The experiments were carried out to measure bubble parameters in a water column using the image visualization technique to determine their inter-relationships and improve the characteristics of surface flow. The data were obtained by processing visualized images of bubble flow structure for the different sections of the bubble regions, and the results confirm that temperature, bubble size, and gas flow rate significantly affect the flow structure and bubble parameters. Full article

We introduce an improved conservative direct re-initialization (ICDR) method (for two-phase flow problems) as a new and efficient geometrical re-distancing scheme. The ICDR technique takes advantage of two mass-conserving and fast re-distancing schemes, as well as a global mass correction concept to reduce the extent of the mass loss/gain in two- and three-dimensional (2D and 3D) problems. We examine the ICDR method, at the first step, with two 2D benchmarks: the notched cylinder and the swirling flow vortex problems. To do so, we (for the first time) extensively analyze the dependency of the regenerated interface quality on both time-step and element sizes. Then, we quantitatively assess the results by employing a defined norm value, which evaluates the deviation from the exact solution. We also present a visual assessment by graphical demonstration of original and regenerated interfaces. In the next step, we investigate the performance of the ICDR in three-dimensional (3D) problems. For this purpose, we simulate drop deformation in a simple shear flow field. We describe our reason for this choice and show that, by employing the ICDR scheme, the results of our analysis comply with the existing numerical and experimental data in the literature. Full article

The present investigation aims to examine the heat flux mechanism in the hagnetohydrodynamic (MHD) mixed convective flow of Williamson-type fluid across an exponential stretching porous curved surface. The significant role of thermal conductivity (variable), non-linear thermal radiation, unequal source-sink, and Joules heating is considered. The governing problems are obtained using the Navier–Stokes theory, and the appropriate similarity transformation is applied to write the partial differential equations in the form of single-variable differential equations. The solutions are obtained by using a MATLAB-based built-in bvp4c package. The vital aspect of this analysis is to observe the effects of the curvature parameter, magnetic number, suction/injection parameter, permeability parameter, Prandtl factor, Eckert factor, non-linear radiation parameter, buoyancy parameter, temperature ratio parameter, Williamson fluid parameter, and thermal conductivity (variable) parameter on the velocity field, thermal distribution, and pressure profile which are discussed in detail using a graphical approach. The correlation with the literature reveals a satisfactory improvement in the existing results on permeability factors in Williamson fluids. Full article

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov–Galerkin projections) if a mixed velocity–pressure formulation is considered, possibly hampering the evaluation of reliable solutions in real-time. Dealing with fluid–structure interactions entails even greater difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning, in a nonintrusive way, both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD, enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid–structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm. Full article

The constant growth of urban agglomerations with the development of transport networks requires the optimal use of energy and new ways of storing it. Energy efficiency is becoming one of the main challenges of modern engineering. The use of phase change materials in construction expands the possibilities of accumulating and storing solar energy, as well as reducing energy consumption. In this study, we consider the problem of the effect of natural convection on heat transfer in a building block containing a phase change material. Heat transfer, taking into account melting in brick, was analyzed at various temperature differences. The mathematical model was formulated in the form of time-dependent equations of conjugate natural convection using non-dimensional stream function, vorticity, and temperature. The equations describing melting, taking into account natural convection, were solved using the finite difference method. Smoothing parameters were used to describe phase transitions in the material. As a result of calculations, local characteristics of heat and mass transfer at various points in time were obtained, as well as changes in temperature profiles on the side surfaces. It is shown that with a large volume of melt, natural convection increases heat loss by more than 10%. Full article

The design of wind turbines requires a deep insight into their complex aerodynamics, such as dynamic stall of a single airfoil and flow vortices. The calculation of the aerodynamic forces on the wind turbine blade at different angles of attack (AOAs) is a fundamental task in the design of the blades. The accurate and efficient calculation of aerodynamic forces (lift and drag) and the prediction of stall of an airfoil are challenging tasks. Computational fluid dynamics (CFD) is able to provide a better understanding of complex flows induced by the rotation of wind turbine blades. A numerical simulation is carried out to determine the aerodynamic characteristics of a single airfoil in a wide range of conditions. Reynolds-averaged Navier–Stokes (RANS) equations and large-eddy simulation (LES) results of flow over a single NACA0012 airfoil are presented in a wide range of AOAs from low lift through stall. Due to the symmetrical nature of airfoils, and also to reduce computational cost, the RANS simulation is performed in the 2D domain. However, the 3D domain is used for the LES calculations with periodical boundary conditions in the spanwise direction. The results obtained are verified and validated against experimental and computational data from previous works. The comparisons of LES and RANS results demonstrate that the RANS model considerably overpredicts the lift and drag of the airfoil at post-stall AOAs because the RANS model is not able to reproduce vorticity diffusion and the formation of the vortex. LES calculations offer good agreement with the experimental measurements. Full article

The spread of renewable resources, such as wind and solar, is one of the main drivers to move from a fossil-based to a renewable-based power generation system. However, wind and solar production are difficult to predict; hence, to avoid a mismatch between electricity supply and demand, there is a need for energy storage units. To this end, new storage concepts have been proposed, and one of the most promising is to store electricity in the form of heat in a Thermal Energy Storage reservoir. However, in Thermal Energy Storage based systems, the critical component is the storage tank and, in particular, its mathematical model as this plays a crucial role in the storage unit performance estimation. Although the literature presents three modelling approaches, each of them differs in the considered parameters and in the method of modelling the fluid and the solid properties. Therefore, there is a need to clarify the model differences and the parameter influences on plant performance as well as to develop a more complete model. For this purpose, the present work first aim is to compare the models available in the literature to identify their strengths and weaknesses. Then, considering that the models’ comparison showed the importance of adopting temperature-dependent fluid and storage material properties to better predict the system performance, the authors developed a new and more detailed model, named TES-PD, which works with time and space variable fluid and solid properties. In addition, the authors included the tank heat losses and the solid effective thermal conductivity to improve the model accuracy. Based on the comparisons between the TES-PD model and the ones available in the literature, the proposal can better predict the first cycle charging time, as it avoids a 4% underestimation. This model also avoids overestimation of the delivery time, delivered energy, mean generated power and plant round-trip efficiency. Therefore, the results underline that a differential and time-accurate model, like the TES-PD, even if one-dimensional, allows a fast and effective prediction of the performance of both the tank and the storage plant. This is essential information for the preliminary design of innovative large-scale storage units operating with thermal storage. Full article

Many complex turbulent flows in nature and engineering can be qualitatively regarded as being constituted of multiple simpler unit flows. The objective of this work is to characterize the coherent structures in such complex flows as a combination of constituent unitary flow structures for the purpose of reduced-order representation. While turbulence is clearly a non-linear phenomenon, we aim to establish the degree to which the optimally weighted superposition of unitary flow structures can represent the complex flow structures. The rationale for investigating such superposition stems from the fact that the large-scale coherent structures are generated by underlying flow instabilities that may be reasonably described using linear analysis. Clearly, the degree of validity of superposition will depend on the flow under consideration. In this work, we take the first step toward establishing a procedure for investigating superposition. Experimental data of single and triple tandem jets in crossflow are used to demonstrate the procedure. A composite triple tandem jet flow field is generated from optimal superposition of single jet data and compared against ‘true’ triple jet data. Direct comparisons between the true and composite fields are made for spatial, temporal, and kinetic energy content. The large-scale features (obtained from proper orthogonal decomposition or POD) of true and composite tandem jet wakes exhibit nearly 70% agreement in terms of modal eigenvector correlation. Corresponding eigenvalues reveal that the kinetic energy of the flow is also emulated with only a slight overprediction. Temporal frequency features are also examined in an effort to completely characterize POD modes. The proposed method serves as a foundation for more rigorous and robust dimensional reduction in complex flows based on unit flow modes. Full article